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Simplifying x2 + 32x + 19 = 0 Reorder the terms: 19 + 32x + x2 = 0 Solving 19 + 32x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-19' to each side of the equation. 19 + 32x + -19 + x2 = 0 + -19 Reorder the terms: 19 + -19 + 32x + x2 = 0 + -19 Combine like terms: 19 + -19 = 0 0 + 32x + x2 = 0 + -19 32x + x2 = 0 + -19 Combine like terms: 0 + -19 = -19 32x + x2 = -19 The x term is 32x. Take half its coefficient (16). Square it (256) and add it to both sides. Add '256' to each side of the equation. 32x + 256 + x2 = -19 + 256 Reorder the terms: 256 + 32x + x2 = -19 + 256 Combine like terms: -19 + 256 = 237 256 + 32x + x2 = 237 Factor a perfect square on the left side: (x + 16)(x + 16) = 237 Calculate the square root of the right side: 15.394804318 Break this problem into two subproblems by setting (x + 16) equal to 15.394804318 and -15.394804318.Subproblem 1
x + 16 = 15.394804318 Simplifying x + 16 = 15.394804318 Reorder the terms: 16 + x = 15.394804318 Solving 16 + x = 15.394804318 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = 15.394804318 + -16 Combine like terms: 16 + -16 = 0 0 + x = 15.394804318 + -16 x = 15.394804318 + -16 Combine like terms: 15.394804318 + -16 = -0.605195682 x = -0.605195682 Simplifying x = -0.605195682Subproblem 2
x + 16 = -15.394804318 Simplifying x + 16 = -15.394804318 Reorder the terms: 16 + x = -15.394804318 Solving 16 + x = -15.394804318 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = -15.394804318 + -16 Combine like terms: 16 + -16 = 0 0 + x = -15.394804318 + -16 x = -15.394804318 + -16 Combine like terms: -15.394804318 + -16 = -31.394804318 x = -31.394804318 Simplifying x = -31.394804318Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.605195682, -31.394804318}
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